Due to the disordered structure of amorphous alloys, the complex structural dynamics involves the particle rearrangements with a large span in time and size scales. The characterization and mechanism of structural dynamics of amorphous alloys are crucial and fundamental for the further research of relaxation behavior and physical aging kinetics of glasses. Abundant researches show that the relaxation spectra of rare-earth-based amorphous alloys, which are represented by lanthanum- and cerium-based alloys, show obvious secondary relaxation process, and the system becomes an ideal carrier to investigate the relationship between structural dynamics and mechanical properties of amorphous alloys. In this review, the anelasticity of metallic glasses was discussed. The anelastic deformation, as the main component of deformation, can totally recovery after unloading in creep experiments, and its mechanism is important to form deep understanding about the structural dynamics of metallic glasses. Additionally, the main characteristics of anelastic deformation during creep and creep recovery were summarized, and some theoretical models for quantitative and qualitative description were introduced.